The question has not been answered and although somewhat dated, I thought I would provide some feedback.
A balun can affect all four scattering parameters. The transformation ratio, the feed characteristic impedance, and the complex load impedance all play a role. It must also be acknowledged that most real world baluns do not perform a linear translation for all complex impedances. This non linearity is difficult to effectively model.
Regarding the "beam pattern", perhaps better described as directivity, can be affected by the balun if the balun effectively prevents common mode currents on the feedline. But to see this effect, the model would need to anticipate radiation (or pickup) by the feedline. This is rarely the case unless the engineer has taken care to build this possibility into the model.